Question

Write the next two terms of the A.P.: ${\displaystyle \sqrt{27},\sqrt{48},\sqrt{75}}$......

Answer 1

Given A.P. is ${\displaystyle \sqrt{27},\sqrt{48},\sqrt{75}}$ ......

Here, a₁ = ${\displaystyle \sqrt{27}=3\sqrt{3}}$

a₂ = ${\displaystyle \sqrt{48}=4\sqrt{3}}$

∴ Common difference = ${\displaystyle 4\sqrt{3}-3\sqrt{3}}$

= ${\displaystyle \sqrt{3}(4-3)=\sqrt{3}}$

Now, Given a₃ = ${\displaystyle \sqrt{75}=5\sqrt{3}}$

∴ a₄ = ${\displaystyle 6\sqrt{3}=\sqrt{108}}$

And a₅ = ${\displaystyle 7\sqrt{3}=\sqrt{147}}$

Hence, next two terms are ${\displaystyle \sqrt{108}}$ and ${\displaystyle \sqrt{147}}$.